While Saffman–Taylor fingers traditionally form due to the injection/withdrawal of one immiscible fluid into another, it is known that these fingers can also be triggered by body forces. The two most commonly studied body forces are gravity and centrifugal forces. For the latter, when the entire Hele–Shaw cell is rotated, this results in the dense viscous fluid being propelled outward which in turn results in fingers forming [1]}. Experimental [2]} and numerical [3]}, [4]}, [5]} studies reveal that the interface patterns are distinct from the traditional Saffman–Taylor instability. That is, fingers appear more `stretched-out' and generally go not undergo tip-splitting. We note that our model (REF )-(REF ) ignores the effect of Coriolis forces, however several studies have investigated its effect on interfacial dynamics [3]}, [1]}, [8]}. Further, we consider the case where the inviscid bubble is injected into the viscous fluid while the plates are rotated in [9]}, where we show that the angular velocity has a stabilising effect on the interface.
